Structure and Spectroscopy of Iron Pentacarbonyl, Fe(CO)5

We have re-investigated the structure and vibrational spectroscopy of the iconic molecule iron pentacarbonyl, Fe(CO)5, in the solid state by neutron scattering methods. In addition to the known C2/c structure, we find that Fe(CO)5 undergoes a displacive ferroelastic phase transition at 105 K to a P1̅ structure. We propose that this is a result of certain intermolecular contacts becoming shorter than the sum of the van der Waals radii, resulting in an increased contribution of electrostatic repulsion to these interactions; this is manifested as a strain that breaks the symmetry of the crystal. Evaluation of the strain in a triclinic crystal required a description of the spontaneous strain in terms of a second-rank tensor, something that is feasible with high-precision powder diffraction data but practically very difficult using strain gauges on a single crystal of such low symmetry. The use of neutron vibrational spectroscopy (which is not subject to selection rules) has allowed the observation of all the fundamentals below 700 cm–1 for the first time. This has resulted in the re-assignment of several of the modes. Surprisingly, density functional theory calculations that were carried out to support the spectral assignments provided a poor description of the spectra.

temperature structures of Fe(CO)5. 10 The crystal structures of Fe(CO)5 phase I at 200 and 110 K, and the structures of Fe(CO)5 phase II at 10 and 100 K are provided as supplementary Crystallographic Information Files (CIFs) and have been deposited with the Cambridge Crystallographic Data Centre. Unit-cell parameters obtained from profile refinements done with the F(calc) weighted method in GSAS are reported in Table S1.
Vibrational spectroscopy. For the INS measurements ~15 g of Fe(CO)5, was loaded into an In wire-sealed Al can. The sample was quenched in liquid nitrogen immediately before insertion into the indirect geometry, high resolution, broad band spectrometer TOSCA 11,12 at ISIS. 3 TOSCA also has a diffraction capability and this was used to confirm that the sample was in the triclinic phase at 10 K. After measurement at ~10 K, the sample was heated to 120 K to measure the monoclinic phase (also confirmed by neutron diffraction).
Raman spectra of the liquid in a quartz cell and after freezing in liquid nitrogen were recorded using a Bruker FT-Raman spectrometer (64 scans at 1 cm -1 resolution with 500 mW laser power at 1064 nm). Variable temperature (7 -300 K) Raman spectra were recorded with a previously described, 13 Renishaw in-Via system using 532 nm excitation.
Infrared spectra (64 scans at 4 cm -1 resolution with eight times zerofilling (to improve the peak shape)) were recorded with a Bruker Vertex 70 FTIR spectrometer. Room temperature spectra of the liquid over the range 50-4000 cm -1 were obtained using the Bruker Diamond ATR accessory and in transmission over the range 350-4000 cm -1 as a CCl4 solution in a KBr cell. Spectra (300-4000 cm -1 ) of the monoclinic phase at 170 K were recorded using a SpecAc Golden Gate variable temperature accessory.
Computational studies. DFT calculations were carried out using three different codes: CASTEP 14 (v17 and v20), DMol3 15 and Gaussian09. 16 For the plane-wave, pseudopotential code CASTEP, exchange and correlation were approximated using the Perdew-Burke-Ernzerhof (PBE) functional, 17  Schmidt 23 (OBS) van der Waals correction was also used. Norm-conserving pseudopotentials were generated by the Optimized Pseudopotential Interface / Unification Module, 24,25 or the in-built on-the-flygenerated (OTFG) pseudopotentials were used. The plane-wave cut-off and Brillouin-zone sampling of electronic states are given in Table S2. The equilibrium structure, an essential prerequisite for lattice dynamics calculations was obtained by Broyden-Fletcher-Goldfarb-Shanno (BFGS) geometry optimization after which the residual forces were converged to zero within ±0.0017 eV Å -1 . Phonon frequencies were obtained by diagonalization of dynamical matrices computed using density-functional perturbation theory 26 (DFPT) for LDA and GGA functionals and by finite displacement for the RSCAN functional. An analysis of the resulting eigenvectors was used to map the computed modes to the corresponding irreducible representations of the point group and assign IUPAC symmetry labels. DFPT was also used to compute the dielectric response and the Born effective charges, and from these the mode oscillator strength tensor and infrared absorptivity were calculated. For DMol3, the BLYP or SCAN functional with a double numerical precision (DNP) basis set was used. For Gaussian09 the B3LYP functional with aug-ccVTZ basis set was used. The INS spectra were generated from the CASTEP output using ACLIMAX. 27

Table S1
Refined unit cell parameters of Fe(CO)5 as a function of temperature. Series 1 consists of measurements made on warming from 10 to 200 K in 10 K increments; series 2 made on cooling from 155 to 55 K in 10 K increments; series 3 made on warming from 100 to 110 K in 2 K increments and then 210 to 240 K in 10 K steps. All entries refer to the C-centred cell. Numbers in parentheses report the estimated standard uncertainty in the last quoted digit. 10 11.61136(5) 6.75987 ( 155 11.72336 (7) 6.79762 (4)

Figure S1
Neutron powder diffraction pattern of Fe(CO)5 measured at 10 K on the HRPD instrument at ISIS. The observations are plotted as filled red circles, the fitted profile refinement as a solid green line, and the difference profile as a solid purple line underneath the Bragg peak markers. The latter are indicated by vertical black lines.

Figure S2
Neutron powder diffraction pattern of Fe(CO)5 measured at 200 K on the HRPD instrument at ISIS. The observations are plotted as filled red circles, the fitted profile refinement as a solid green line, and the difference profile as a solid purple line underneath the Bragg peak markers. The latter are indicated by vertical black lines.

Figure S3
Elements, eij, of the spontaneous strain tensor as a function of temperature, corresponding with the strain resulting from the ferroelastic transition from the C2/c to 1 � structure on cooling of Fe(CO)5. The panel on the left emphasises the large symmetry-breaking strains, e12 and e23. The panel on the right offers an expanded view to highlight the linear dependence on T of the weak non symmetry-breaking strains.

Figure S4
Representation surface of the spontaneous strain tensor, evaluated at 75 K. The lobes coloured in red indicate negative tensile strain along the principal direction e1; the lobes in green indicate positive tensile strain along the principal direction e3. The orthogonal axes are related to the crystallographic axes of the Ccentred cell by, x || a*, y || b, z || c. The spatial relationship of this figure to the crystal structure is shown in the main text, Figure 5. Drawn using WinTensor 28

Figure S5
Another proxy for the spontaneous strain element e23, that may be calculated without recourse to extrapolation of the high-temperature unit-cell parameters, is cos 2 (α*), where the * denotes the reciprocal lattice. The panel on the left shows the linear relationship between cos 2 (α*) and temperature, with an intercept at TC = 104.6(3) K. The panel on the right shows the perfectly linear relationship between cos(γ) and cos(α*) in the range of temperatures from 70 -100 K, indicating that a single order parameter, Q, is responsible for both the e12 and e23 strains with comparable degrees of coupling.

Figure S6
Fingerprint plots derived from calculated Hirschfeld surfaces. The contributions from different intermolecular contacts are shown as a function of temperature; these are the C···O contacts and their reciprocal O···C contacts, O···O contacts and C···C contacts. For each panel, the fractional contribution to the total surface area of the Hirschfeld surface is reported.

Figure S7
Hirschfeld surfaces of the Fe(CO)5 molecule at temperatures corresponding with the four structural refinements reported in this work. Surfaces are shaded by dnorm values, with white and blue corresponding to distances that are equal to, or longer than, the sum of the van der Waals radii. Patches of red colour correspond with distances shorter than the van der Waals radii sum.

Table S3
Energies associated with each of the interactions depicted in Figure S8, evaluated at 200 K, using the same colour-coding scheme. The energies are broken down into electrostatic (Eele), polarisation (Epol), dispersion (Edis) and exchange-repulsion (Erep) contributions. The total energy of each interaction is Etot. R is the distance between molecular centres.

Table S4
Temperature dependence of the interaction energies for the first nearest neighbour interaction, 0-1.

Table S5
Temperature dependence of the interaction energies for the second nearest neighbour interaction, 0-2. Note the substantially larger value of the ratio Erep / Edis for this interaction compared with the other two strong stabilising interactions in the crystal (cf., Tables S4 and S6).

Table S6
Temperature dependence of the interaction energies for the third nearest neighbour interaction, 0-3.

Thermal expansion analysis
Eulerian infinitesimal strain tensors were calculated from pairs of cell parameters determined at adjacent temperature and then normalised by the temperature increment between them in order to obtain thermal expansion tensors, i.e., unit-strain tensors (cf. 29 ). Standard matrix decomposition methods 30 were used to derive the eigenvalues and eigenvectors of the thermal expansion tensor, these being the magnitudes and orientations of the principal expansivities.
The temperature dependences of the three principal linear expansivities are shown in Figure   S8, revealing the involvement of the spontaneous strain in dominating the linear thermal expansion terms α1 and α2. Above the transition, in the absence of the spontaneous strain, we see that the underlying framework expansivity is only moderately anisotropic ( Figure S8d).
The principal direction α2 for the monoclinic phase of Fe(CO)5 is constrained by symmetry to coincide with the 2-fold axis, whilst α1 and α3 need not be aligned with any particular crystallographic direction; in fact, the direction of greatest thermal expansion above 110 K, α3, is approximately parallel with c*. In the low-temperature triclinic phase of Fe(CO)5 the orientation of the thermal expansion tensor has no such symmetry constraints and the principal directions do not necessarily co-align with any particular direction. However, α1 and α2 are co-planar with the spontaneous strains e1 and e3, lying approximately in the (1 � 01) plane. Figure S9 shows the spatial relationship between the thermal expansion tensor representations (cf. 31 ) above and below the ferroelastic transition and the spontaneous strain tensor representation below the transition.

Figure S10
Comparison of the tensor representation surfaces describing (a) the spontaneous strain at 75 K, WinTensor. 28 The temperature dependence of the volume thermal expansion is plotted in Figure S10. The large anomalies present in the principal expansivities largely cancel out and the volume expansion is a smoothly varying function from 10 -240 K, as one might expect for a second-order phase transition. This agrees with the lack of any observed anomaly in the specific heat capacity. 32

Figure S11
Volume thermal expansion of Fe(CO)5.
The unit-cell volumes of Fe(CO)5, in both the low-and high-temperature forms, have been fitted with a second-order Grüneisen approximation to the zero-pressure equation of state. 33 In this approximation, the thermal expansion is considered equivalent to elastic strain such that, where V0 is the unit cell volume at zero pressure, b = ½ ( 0 ′ −1) and Q = (V0 K0/γ); K0 is the zeropressure isothermal bulk modulus, 0 ′ is its first derivative with respect to pressure, and γ is the thermal Grüneisen parameter. The internal energy due to lattice vibrations, E(T), is then determined via a simple Debye model approximation of the phonon density of states: where θD is the Debye temperature, n is the number of atoms per unit cell, and kB is the Boltzmann constant; the integral term is evaluated numerically. Table S4 reports the parameters obtained from fitting equations 1 to the unit-cell volumes of Fe(CO)5. These correspond with the solid red line on Figure S11.   (1) Bond angles (°)  19 functional. c GGA = generalized gradient approximation. LDA = local gradient approximation. meta-GGA = meta generalized gradient approximation. d OTFG = on-the-fly-generated pseudopotential. Opium = norm-conserving pseudopotentials generated by the Optimized Pseudopotential Interface / Unification Module. 24,25

Additional Supplementary Information
Crystallographic Information Files (CIFs) reporting the atomic coordinates and anisotropic displacement parameters at 10, 100, 110 and 200 K. These include additional quantitative information about the measurements and the refinements, and also contain the observed and calculated neutron powder diffraction patterns.
These files are deposited with the Cambridge Structural Database and may be accessed using the following codes.